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**1 - 4**of**4**### ARISTOTELIAN REALISM

"... Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as rat ..."

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Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity,

### What is Neologicism? 2 What is Neologicism? ∗

"... Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that ..."

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Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that

### On the Logic of Quantifier Variance

"... Eli Hirsch recently suggested the metaontological doctrine of so-called quantifier variance, according to which ontological disputes—e.g. concerning the question whether arbitrary, possibly scattered, mereological fusions exist, in the sense that these are recognised as objects in our ontology—can b ..."

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Eli Hirsch recently suggested the metaontological doctrine of so-called quantifier variance, according to which ontological disputes—e.g. concerning the question whether arbitrary, possibly scattered, mereological fusions exist, in the sense that these are recognised as objects in our ontology—can be defused as insubstantial. His proposal is that the meaning of the quantifier ‘there exists ’ varies in such debates: according to one opponent in this dispute, some existential statement claiming the existence of, e.g., a scattered object is true, according to the other it is not. This paper argues that Hirsch’s proposal leads into inconsistency. The term ‘metaontology ’ has recently been coined for a well-established field in metaphysics. As Matti Eklund put it succinctly in the introductory remarks of his (Eklund, 2006a, 317): “Ontology is the study of what there